Question

Use the power rule of exponents to simplify (10^3)^6
1) 10^9
2) 10^6
3) 10^3
4) 10^18
Answer
what is the missing number in this simplified expression: 7^? divided 7^5 =7^12?
1) 7
2) 17
3) 5
4) 12
Answer
Use the power rule of exponents to create a simplified equivalent expression for (19^4)^9
1) 19^36
2) 19^13
3) 19^9
4) 19^5
Answer
apply the product rule of integer exponents to find the numercial equivalent of 12^-5.12^7
1) 12
2) 144
3)-12
4)-144
Answer
what is the value of 6.9-2^0?
1) 4.9
2) 0
3) 5.9
4) 6.9
Answer
what is the missing exponent in the following equations h^450/h^? = h^215
1) 215
2) 235
3) 225
4) 205
Answered by GPT-4o mini
To simplify \((10^3)^6\) using the power rule of exponents, which states that \((a^m)^n = a^{m \cdot n}\), we can apply it as follows:

\[
(10^3)^6 = 10^{3 \cdot 6} = 10^{18}
\]

Thus, the simplified form is \(10^{18}\).

The correct answer is:
4) \(10^{18}\)
Answered by GPT-4o mini
To solve for the missing exponent in the expression \(\frac{7^?}{7^5} = 7^{12}\), we can use the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\).

Setting up the equation, we have:

\[
\frac{7^?}{7^5} = 7^{? - 5}
\]

We set this equal to \(7^{12}\):

\[
7^{? - 5} = 7^{12}
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
? - 5 = 12
\]

Now, solving for \(?\):

\[
? = 12 + 5
\]
\[
? = 17
\]

So, the missing number is **17**.

The correct answer is:
2) 17
Answered by GPT-4o mini
To simplify \((19^4)^9\) using the power rule of exponents, which states that \((a^m)^n = a^{m \cdot n}\), we apply it as follows:

\[
(19^4)^9 = 19^{4 \cdot 9} = 19^{36}
\]

Thus, the simplified equivalent expression is \(19^{36}\).

The correct answer is:
1) \(19^{36}\)
Answered by GPT-4o mini
To apply the product rule of integer exponents, which states that \(a^m \cdot a^n = a^{m+n}\), we can simplify \(12^{-5} \cdot 12^{7}\) as follows:

\[
12^{-5} \cdot 12^{7} = 12^{-5 + 7} = 12^{2}
\]

Now, calculating \(12^2\):

\[
12^2 = 144
\]

Thus, the numerical equivalent of \(12^{-5} \cdot 12^{7}\) is \(144\).

The correct answer is:
2) \(144\)
Answered by GPT-4o mini
To solve the expression \(6.9 - 2^0\), first we need to evaluate \(2^0\).

According to the properties of exponents, any non-zero number raised to the power of \(0\) is \(1\). Therefore:

\[
2^0 = 1
\]

Now, we can substitute this value back into the expression:

\[
6.9 - 1 = 5.9
\]

So the value of \(6.9 - 2^0\) is \(5.9\).

The correct answer is:
3) \(5.9\)
Answered by GPT-4o mini
To solve for the missing exponent in the equation \( \frac{h^{450}}{h^{?}} = h^{215} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

Setting up the equation, we have:

\[
\frac{h^{450}}{h^{?}} = h^{450 - ?}
\]

We set this equal to \( h^{215} \):

\[
h^{450 - ?} = h^{215}
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
450 - ? = 215
\]

Now, solving for \( ? \):

\[
? = 450 - 215 = 235
\]

Thus, the missing exponent is **235**.

The correct answer is:
2) 235